ANN ARBOR, Mich. (AP)--DeShawn Sims scored a career-high 29 points and Manny Harris had 27 points and eight rebounds to lead Michigan to an 87-78 victory over No. 16 Purdue on Thursday night.

The Wolverines (18-11, 8-8 Big Ten) improved to 3-4 against ranked opponents and added an important victory to the ones it had over Duke and UCLA, when both teams were ranked fourth in the nation. Michigan is trying for its first NCAA tournament bid in more than a decade.

Purdue, which had won four straight, fell two games behind Big Ten-leading Michigan State and a half-game behind Illinois.

The Boilermakers trailed by three midway through the second half, but couldn't stop Sims or Harris during a 19-6 run that decided the game.

The Wolverines haven't earned an NCAA tournament bid since 1998, but they've got a shot to end the drought with two talented upperclassmen--Sims and Harris -- recruited by former coach Tommy Amaker, gutsy freshmen and savvy coaching by John Beilein, who is in his second season.

Michigan was coming off a deflating loss to Iowa, the 10th-place team in the Big Ten, in which Harris was benched during the overtime. But Harris and the Wolverines bounced back with an inspired effort in their regular-season home finale.

Harris became the sixth player in Michigan history to reach the 1,000-point mark as a sophomore, joining Chris Webber, Jalen Rose, Phil Hubbard, Mike McGee and Louis Bullock.

The shooting guard forced Purdue to extend its defense with his outside shooting.

Boilermakers coach Matt Painter, meanwhile, struggled to defend Sims inside because 6-foot-10 forward JaJuan Johnson had three fouls midway through the first half and was called for a fourth early in the second.

After taking a 16-point lead with 4 1/2 minutes left, Michigan added some drama because it missed the front end of some 1-and-1 opportunities and missed a slew of other free throws in the closing minutes.

The Wolverines were 11-of-21 at the line in the second half, giving Purdue a glimmer of hope.

Purdue hurt its Big Ten title chances, but the team can be encouraged by the play of Hummel. He fell only one point of his career high, showing he seems to be regaining his form after missing three games earlier this month with a fracture in his lower back.